Given two imaginary points. Construct the line connecting the points.
The two points are each one of the double points of an elliptic involution on a line. These evolutions are respresented by an arrow on the carrier of these points. Vector A and vector B (in red)
A semi circle is constructed on the amplitude of the involutions.
On lina a: Take the intersection of a and b as . Draw and perpendicular. and are inner and outer bisectrixes of triangle
The four points are two pairs of points in the given involution.
Likewise for point B and the four points and
The two ranges of four points X an Y are perspective both from M and from N

In N four lines determine an elliptic involution, of wich the two imaginary double lines are the lines that connect the imaginary points A and B.
Because The elliptic involution on line a has two double points and , (Likewise B on b.) we have four
connecting imaginary lines.
Two in N: and
and two in M: and